Question: Solve for $x$ and $y$ using elimination. ${3x+5y = 20}$ ${-3x-2y = -17}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. $3y = 3$ $\dfrac{3y}{{3}} = \dfrac{3}{{3}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {3x+5y = 20}\thinspace$ to find $x$ ${3x + 5}{(1)}{= 20}$ $3x+5 = 20$ $3x+5{-5} = 20{-5}$ $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {-3x-2y = -17}\thinspace$ and get the same answer for $x$ : ${-3x - 2}{(1)}{= -17}$ ${x = 5}$